Tag: rational numbers as recurring/terminating decimals

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Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

$0.\overline{585}$ is equal to

  1. $\displaystyle\frac{585}{99}$
  2. $\displaystyle\frac{585}{999}$
  3. $\displaystyle\frac{999}{585}$

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given that, $0.\overline{585}$.

Let,

$ x=0.\overline{585} $

$ x=0.585585585........ $

 

Multiply by 1000 on both sides,

$ 1000x=1000\times 0.585585585........ $

$ =585.585585585.... $

$ =585+0.585585585........ $

$ 1000x=585+x $

$ 999x=585 $

$ x=\dfrac{585}{999} $

 

Hence, this is the answer.

Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

If the quotient is terminating decimal, the division is complete only when ...............

  1. we get the remainder $1$

  2. we get the remainder zero

  3. we get the remainder as the repeated numbers

  4. All of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Any division is complete only when we get the remainder zero.
Therefore, $B$ is the correct answer.
Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

Which option will have a terminating decimal expansion?

  1. $\dfrac {77}{210}$
  2. $\dfrac {23}{30}$
  3. $\dfrac {125}{441}$
  4. $\dfrac {23}{8}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The decimal expansion of a number may terminate in which case the number is called a regular number or finite decimal. In the given options:

a. $\dfrac{77}{210} = 0.366666666....... \; or  \; 0.3\bar6$

b. $\dfrac{23}{30} = 0.766666666....... \; or  \; 0.7\bar6$

c. $\dfrac{125}{441} = 0.283446712......$ i.e. it goes on infintely

d. $\dfrac{23}{8} = 2.875$

Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

A number having non-terminating and recurring decimal expansion is.

  1. An integer

  2. A rational number

  3. An irrational number

  4. A whole number
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A number having non-terminating and recurring decimal expansion is  a Rational Number


for example 

$\dfrac{2}{7}$  is a rational number 

$\dfrac{2}{7} =0.285714285714285714.......... $

or   $\dfrac{2}{7} =\overline{0.285714}.......... $

the number has non-terminating decimal expansion but recurring after every 6 digits after decimal

So option $B $ is correct

Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

Which of the following numbers has the terminating decimal representation?

  1. $\displaystyle \frac{1}{7}$
  2. $\displaystyle \frac{1}{3}$
  3. $\displaystyle \frac{3}{5}$
  4. $\displaystyle \frac{17}{3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\dfrac{3}{5} = 0.6$ which is terminating decimal. 


$\dfrac{1}{7} = 0.142857.....$

$\dfrac{1}{3} = 0.333......$

$\dfrac{17}{3} = 5.6666......$

Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

Show the correct sequence of the given four option in ascending order
(1) Prime minister  (2) Chief Minister  (3) Mayor  (4) President  (5) Sarpanch

  1. $5,3,2,4,1$
  2. $5,2,3,4,1$
  3. $5,3,2,1,4$
  4. $5,4,2,1,3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
In ascending order 
Sarpanch < Mayore < Chief Minister < Prime minister < President.
$\therefore$ Option $ C$  is the correct answer.